Double Neimark-Sacker bifurcation and torus bifurcation of a class of vibratory systems with symmetrical rigid stops

Journal of Sound and Vibration

Volumn 298, Issue 1-2, 2006, Pages 154-179

  Luo, G W ^a   Chu, Y D ^a   Zhang, Y L ^a   Zhang, J G ^a  

^a LANZHOU JIAOTONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); ELECTRIC EXCITATION; LINEAR SYSTEMS; MAPS; MATHEMATICAL MODELS; PARAMETER ESTIMATION; THRESHOLD ELEMENTS;

AMPLITUDE CONSTRAINTS; NEIMARK-SACKER BIFURCATION; QUASI-PERIODIC IMPACT MOTIONS; VIBRATORY SYSTEMS;

VIBRATIONS (MECHANICAL);

EID: 33748081103     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2006.04.025     Document Type: Article

References (53)

1. Holmes P.J. The dynamics of repeated impacts with a sinusoidally vibrating table. Journal of Sound and Vibration 84 2 (1982) 173-189
2. Shaw S.W., and Holmes P.J. A periodically forced piecewise linear oscillator. Journal of Sound and Vibration 90 1 (1983) 129-155
3. Shaw S.W. The dynamics of a harmonically excited system having rigid amplitude constraints: part 1, part 2. Journal of Applied Mechanics 52 (1985) 453-464
4. Whiston G.S. Global dynamics of vibro-impacting linear oscillator. Journal of Sound and Vibration 118 3 (1987) 395-429
5. Yim C.S., and Lin H. Nonlinear impact and chaotic response of slender rocking objects. Journal of Engineering. Mechanics 117 9 (1991) 2079-2100
6. de Souza S.L.T., and Caldas I.L. Calculation of Lyapunov exponents in systems with impacts. Chaos, Solitons and Fractals 19 3 (2004) 569-579
7. Aidanpää J.O., and Gupta B.R. Periodic and chaotic behaviour of a threshold- limited two-degree-of-freedom system. Journal of Sound and Vibration 165 2 (1993) 305-327
8. Wagg D.J. Rising phenomena and the multi-sliding bifurcation in a two-degree of freedom impact oscillator. Chaos, Solitons and Fractals 22 3 (2004) 541-548
9. Cone K.M., and Zadoks R.I. An numerical study of an impact oscillator with the addition of dry friction. Journal of Sound and Vibration 188 5 (1995) 659-683
10. Jin D.P., and Hu H.Y. Periodic vibro-impacts and their stability of a dual component system. Acta Mechanism Sinica 13 4 (1997) 366-376
11. Nordmark A.B. Non-periodic motion caused by grazing incidence in an impact oscillator. Journal of Sound and Vibration 145 2 (1991) 279-297
12. Whiston G.S. Singularities in virbo-impact dynamics. Journal of Sound and Vibration 152 3 (1992) 427-460
13. Foale S., and Bishop S.R. Dynamical complexities of forced impacting systems. Philosophical Transactions of the Royal Society of London 338 A (1992) 547-556
14. Ivanov A.P. Bifurcation in impact systems. Chaos, Solitons and Fractal 7 10 (1996) 1615-1634
15. Peterka F. Bifurcation and transition phenomena in an impact oscillator. Chaos, Solitons and Fractals 7 10 (1996) 1635-1647
16. Peterka F., and Vacik J. Transition to chaotic motion in mechanical systems with impacts. Journal of Sound and Vibration 154 1 (1992) 95-115
17. Budd C., Dux F., and Cliffe A. The effect of frequency and clearance variations on single-degree- of-freedom impact oscillators. Journal of Sound and Vibration 184 3 (1995) 475-502
18. Feigin M.I. The increasingly complex structure of the bifurcation tree of a piecewise-smooth system. Journal of Applied Mathematics and Mechanics 59 6 (1995) 853-863
19. Bernardo D., Feigin M.I., Hogan S.J., and Homer M.E. Local analysis of C-bifurcations in N-dimensional piecewise-smooth dynamical systems. Chaos, Solitons and Fractals 10 11 (1999) 1881-1908
20. Nguyen D.T., Noah S.T., and Kettleborough C.F. Impact behaviour of an oscillator with limiting stops, part I: a parametric study. Journal of Sound and Vibration 109 2 (1986) 293-307
21. Natsiavas S. Dynamics of multiple-degree-of-freedom oscillators with colliding components. Journal of Sound and Vibration 165 3 (1993) 439-453
22. Chatterjee S., and Mallik A.K. Bifurcations and chaos in autonomous self-excited oscillators with impact damping. Journal of Sound and Vibration 191 4 (1996) 539-562
23. Luo G.W., and Xie J.H. Hopf bifurcation of a two-degree-of-freedom vibro-impact system. Journal of Sound and Vibration 213 3 (1998) 391-408
24. Luo G.W., and Xie J.H. Stability of periodic motion, bifurcations and chaos of a two-degree-of-freedom vibratory system with symmetrical rigid stops. Journal of Sound and Vibration 273 2 (2004) 543-568
25. Hu H.Y. Controlling chaos of a periodically forced nonsmooth mechanical system. Acta Mechanica Sinica 11 3 (1995) 251-258
26. Mejaard J.P., and De Pater A.D. Railway vehicle systems dynamics and chaotic vibrations. International Journal of Non-Linear Mechanics 24 1 (1989) 1-17
27. Zeng J., and Hu S. Study on frictional impact and derailment for wheel and rail. Journal of Vibration Engineering 14 1 (2001) 1-6
28. True H. Dynamics of a rolling wheelset. Applied Mechanics Reviews 46 7 (1993) 438-444
29. Wood L.A., and Byrne K.P. Analysis of a random repeated impact process. Journal of Sound and Vibration 78 3 (1981) 329-345
30. Huang Z.L., Liu Z.H., and Zhu W.Q. Stationary response of multi-degree-of-freedom vibro-impact systems under white noise excitations. Journal of Sound and Vibration 275 1-2 (2004) 223-240
31. Shu Z.Z., and Shen X.Z. Theoretical analysis of complete stability and automatic vibration isolation of impacting and vibrating systems with double masses. Chinese Journal of Mechanical Engineering 26 3 (1990) 50-57
32. Kozol J.E., and Brach R.M. Two-dimensional vibratory impact and chaos. Journal of Sound and Vibration 148 2 (1991) 319-327
33. Xie J.H. The mathematical model for the impact hammer and global bifurcations. Acta Mechanica Sinica 29 4 (1997) 456-463
34. Thompson J.M.T. Complex dynamics of compliant offshore structures. Proceedings of the Royal Society of London A 387 (1983) 407-427
35. Sung C.K., and Yu W.S. Dynamics of harmonically excited impact damper: bifurcations and chaotic motion. Journal of Sound and Vibration 158 2 (1992) 317-329
36. Bapat C.N., and Bapat C. Impact-pair under periodic excitation. Journal of Sound and Vibration 120 1 (1988) 53-61
37. Han P.R.S., and Luo A.C.J. Chaotic motion of a horizontal impact pair. Journal of Sound and Vibration 181 2 (1995) 231-250
38. Heiman M.S., Bajaj A.K., and Sherman P.J. Periodic motions and bifurcations in dynamics of an inclined impact pair. Journal of Sound and Vibration 124 1 (1988) 55-78
39. Bapat C.N. The general motion of an inclined impact damper with friction. Journal of Sound and Vibration 184 3 (1995) 417-427
40. Luo A.C.J. An unsymmetrical motion in a horizontal impact oscillator. Journal of Vibration and Acoustics, Transactions of the ASME 124 3 (2002) 420-426
41. Kahraman A., and Singh R. Non-linear dynamics of a geared rotor-bearing system with multiple clearances. Journal of Sound and Vibration 144 3 (1991) 469-506
42. Kunert A., and Pfeiffer F. Stochastic model for rattling in gear-boxes. Nonlinear dynamics in engineering system. In: Schiehlen W. (Ed). Nonlinear Dynamics in Engineering Systems (1990), Springer, Berlin, Heidelberg 173-180
43. Lin T.J., Li R.F., and Tao Z.G. Numerical simulation of 3-D gap type nonlinear dynamic contact-impact characteristics for gear transmission. Chinese Journal of Mechanical Engineering 36 6 (2000) 55-58
44. Dong H.J., Shen Y.W., Liu M.G., and Zhang S.H. Research on the dynamical behaviors of rattling in gear system. Chinese Journal of Mechanical Engineering 40 1 (2004) 136-141
45. Guckenheimer J., and Holmes P.J. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. second printing (1986), Springer, New York, Berlin, Heidelberg, Tokyo
46. Kuznetsov Y.A. Elements of Applied Bifurcation Theory (1998), Springer, New York
47. Wiggins S. An Introduction to Applied Nonlinear Dynamical Systems and Chaos (1990), Springer, Berlin
48. Arrowsmith D.K., and Place C.M. An Introduction to Dynamical Systems (1990), Cambridge University Press, Cambridge
49. Carr J. Applications of Centre Manifold Theory. Applied Mathematical Sciences, Vol. 35 (1981), Springer, Berling, Heidelberg, New York
50. B.D. Hassard, N.D. Kazarinoff, Y.H. Wan, Theory and Applications of Hopf Bifurcation, London Mathematical Society Lecture Note Series, Vol. 41, 1981.
51. Rogers R.J., and Pick R.J. On the dynamic spatial response of a heat exchanger tube with intermittent baffle contacts. Nuclear Engineering and Design 36 (1976) 81-90
52. Wen B.C., and Liu F.Q. Theory and Application of Vibratory Mechanism (1982), Mechanism Industry Press, Beijing, China
53. Wen B.C., Li Y.L., and Han Q.K. Theory and Application of Nonlinear Oscillation (2001), Northeast University Press, Shenyang, China